Taylor Swift Obsessed Fan Busted, Hangin' On Roof, Buzzin' the Bell

Taylor Swift should be super secure in her $20 million fortified NYC penthouse, but it didn't stop an obsessed fan from wreaking some serious havoc.

29-year-old Mohammed Jaffar was hell-bent on getting a face-to-face with the singer, and according to legal docs obtained by the NY Post he was all over her building ... in the lobby and on the roof.

He showed up multiple times over the last few months, hanging out on the roof one night between 10 PM and 2 AM.

He rang her doorbell incessantly ... once for an hour straight.

Jarffar was arrested for stalking and burglary and he's being held on $20k bond.